Subtraction of Unlike Fractions

We will learn how to solve subtraction of unlike fractions. In order to subtract unlike fractions first we convert them as like fractions.

To subtract unlike fractions, we first convert them into like fractions. In order to make a common denominator, we find LCM of all the different denominators of given fractions and then make them equivalent fractions with a common denominators.

Let us consider some of the examples of subtracting unlike fractions:

1. Subtract 1/10 from 2/5.

Solution:

2/5 - 1/10

The L.C.M. of the denominators 10 and 5 is 10.

2/5 = (2 × 2)/(5 × 2) = 4/10, (because 10 ÷ 5 = 2)

1/10 = (1 × 1)/(10 × 1) = 1/10, (because 10 ÷ 10 = 1)

Thus, 2/5 - 1/10

= 4/10 - 1/10

= (4 - 1)/10

= 3/10


2. Subtract \(\frac{3}{8}\) from \(\frac{5}{12}\).

Solution:

Let us find the LCM of denominators 8 and 12. LCM is 24.

\(\frac{3}{8}\) = \(\frac{3 × 3}{8 × 3}\) = \(\frac{9}{24}\) and

\(\frac{5}{12}\) = \(\frac{5 × 2}{12 × 2}\) = \(\frac{10}{24}\)

Now, subtract \(\frac{9}{24}\) and \(\frac{10}{24}\).

\(\frac{10}{24}\) - \(\frac{9}{24}\)                                    

= \(\frac{10 - 9}{24}\)

= \(\frac{1}{24}\)

Let us illustrate the above example pictorially as shown below.

Subtraction of Fractions

The whole strip above has 24 equal parts. The fraction \(\frac{5}{12}\) is equal to \(\frac{10}{24}\). So the shaded portion represents \(\frac{10}{24}\). We take away \(\frac{3}{8}\) or \(\frac{9}{24}\) of the above strip. The remaining part represents \(\frac{1}{24}\) of the whole strip.


3. Subtract 4/9 from 5/7.

Solution:

5/7 - 4/9

The L.C.M. of the denominators 9 and 7 is 63.

5/7 = (5 × 9)/(7 × 9) = 45/63, (because 63 ÷ 7 = 9)

4/9 = (4 × 7)/(9 × 7) = 28/63, (because 63 ÷ 9 = 7)

Thus, 5/7 - 4/9

= 45/63 - 28/63

= (45 - 28)/63

= 17/63


4. Subtract 5/8 from 1.

Solution:

1 - 5/8

= 1/1 - 5/8

The L.C.M. of the denominators 1 and 8 is 8.

1/1 = (1 × 8)/(1 × 8) = 8/8, (because 8 ÷ 1 = 8)

5/8 = (5 × 1)/(8 × 1) = 5/8, (because 8 ÷ 8 = 1)

Thus, 1/1 - 5/8

= 8/8 - 5/8

= (8 - 5)/8

= 3/8

 

5. Subtract 19/36 from 23/24.

Solution:

23/24 - 19/36

The L.C.M. of the denominators 24 and 36 is 72.

23/24 = (23 × 3)/(24 × 3) = 69/72, (because 72 ÷ 24 = 3)

19/36 = (19 × 2)/(36 × 2) = 38/72, (because 72 ÷ 36 = 2)

Thus, 23/24 - 19/36

= 69/72 - 38/72

= (69 - 38)/72

= 31/72


6. Subtract 9/35 from 3/7.

Solution:

3/7 - 9/35

The L.C.M. of the denominators 7 and 35 is 35.

3/7 = (3 × 5)/(7 × 5) = 15/35, (because 35 ÷ 7 = 5)

9/35 = (9 × 1)/(35 × 1) = 9/35, (because 35 ÷ 35 = 1)

Thus, 3/7 - 9/35

= 15/35 - 9/35

= (15 - 9)/35

= 6/35 

Subtraction of Unlike Fractions


7. Subtract \(\frac{2}{5}\) from 7.

Solution:

\(\frac{7}{1}\) - \(\frac{2}{5}\)

= \(\frac{7  × 5 - 2 × 1}{5}\) LCM of 1 and 5 is 5

= \(\frac{35 -2}{5}\)

= \(\frac{33}{5}\)

= 6\(\frac{3}{5}\)

Hence, 7 - \(\frac{2}{5}\) = 6\(\frac{3}{5}\)


Note: We write the whole number in the fraction form by keeping 1 in the denominator.


Subtraction of Fractions having the Different Denominator:

8. Subtract \(\frac{2}{3}\) - \(\frac{1}{4}\)

\(\frac{2}{3}\) = \(\frac{8}{12}\) [\(\frac{2 × 4}{3 × 4}\) = \(\frac{8}{12}\)]

\(\frac{1}{4}\) = \(\frac{3}{12}\) [\(\frac{1 × 3}{4 × 3}\) = \(\frac{3}{12}\)]

\(\frac{2}{3}\) - \(\frac{1}{4}\) = \(\frac{8}{12}\) - \(\frac{3}{12}\)

= \(\frac{8 - 3}{12}\)

= \(\frac{5}{12}\)

Method 1:

Step I: Find the L.C.M. of the denominators 3 and 4.

L.C.M. of 3 and 4 is 12

Step II: Write the equivalent fractions of \(\frac{2}{3}\) and \(\frac{1}{4}\) with denominator 12.

Step III: Subtract

Step IV: Write the difference in lowest terms.


9. Subtract \(\frac{5}{6}\) - \(\frac{1}{8}\)

\(\frac{5}{6}\) - \(\frac{1}{8}\) = \(\frac{(24 ÷ 6) × 5 – (24 ÷ 8) × 1}{24}\)

= \(\frac{(4 × 5) – (3 × 1)}{24}\)

= \(\frac{20 - 3}{24}\)

= \(\frac{17}{24}\)


Method 2:

L.C.M. of 6 and 8


Subtraction of Mixed Numbers:

Method I:

Subtract 8\(\frac{1}{2}\) - 3\(\frac{1}{4}\)

8\(\frac{1}{2}\) - 3\(\frac{1}{4}\) = (8 – 3) + [\(\frac{1}{2}\) - \(\frac{1}{4}\)]

= 5 + [\(\frac{1}{2}\) - \(\frac{1}{4}\)]

= 5 + [\(\frac{2}{4}\) - \(\frac{1}{4}\)]

= 5 + \(\frac{1}{4}\)

= 5\(\frac{1}{4}\)

Method II:

Subtract 8\(\frac{1}{2}\) - 3\(\frac{1}{4}\)

L.C.M. of 4 and 2 is 4.

8\(\frac{1}{2}\) - 3\(\frac{1}{4}\) = \(\frac{17}{2}\) - \(\frac{13}{4}\)

= \(\frac{34}{4}\) - \(\frac{13}{4}\)

= \(\frac{34 - 13}{4}\)]

= \(\frac{21}{4}\)

= 5\(\frac{1}{4}\)


2. What is 1\(\frac{4}{5}\) less than 4\(\frac{1}{2}\)?

Find 4\(\frac{1}{2}\) - 1\(\frac{4}{5}\)

4\(\frac{1}{2}\) - 1\(\frac{4}{5}\) = \(\frac{9}{2}\) - \(\frac{9}{5}\)            L.C.M. of 2 and 5 is 10.

             = \(\frac{45}{10}\) - \(\frac{18}{10}\)

             = \(\frac{45 - 18}{10}\)

             = \(\frac{27}{10}\)

            = 2\(\frac{7}{10}\)



Questions and Answers on Subtraction of Unlike Fractions:

1. Find the difference:

(i) \(\frac{3}{8}\) - \(\frac{1}{8}\)

(ii) \(\frac{17}{23}\) - \(\frac{6}{23}\)

(iii) \(\frac{1}{2}\) - \(\frac{3}{16}\)

(iv) \(\frac{5}{14}\) - \(\frac{2}{7}\)

(v) \(\frac{5}{6}\) - \(\frac{3}{4}\)

(vi) \(\frac{2}{3}\) - \(\frac{1}{5}\)

(vii) 5 - \(\frac{3}{4}\)

(viii) 2 - \(\frac{15}{21}\)

(ix) 4\(\frac{2}{3}\) - 2



Answers:

1. (i) \(\frac{1}{4}\)

(ii) \(\frac{11}{23}\)

(iii) \(\frac{5}{16}\)

(iv) \(\frac{1}{14}\)

(v) \(\frac{1}{12}\)

(vi) \(\frac{7}{15}\)

(vii) \(\frac{17}{4}\)

(viii) \(\frac{27}{21}\)

(ix) 2\(\frac{2}{3}\)


2. Subtract the following Unlike Fractions:

(i) \(\frac{4}{7}\) - \(\frac{1}{3}\)

(ii) \(\frac{3}{4}\) - \(\frac{1}{2}\)

(iii) 8 - \(\frac{2}{3}\)

(iv) 1\(\frac{5}{6}\) - 1\(\frac{1}{2}\)

(v) 4\(\frac{3}{4}\) - \(\frac{1}{2}\)

(vi) 2\(\frac{1}{3}\) - 1\(\frac{1}{2}\)

(vii) 13\(\frac{4}{7}\) - 6

(viii) 7\(\frac{2}{5}\) - 3\(\frac{1}{2}\)

(ix) \(\frac{9}{2}\) - 4

(x) \(\frac{2}{5}\) - \(\frac{3}{10}\)


Answer: 

2. (i) \(\frac{5}{21}\)

(ii) \(\frac{1}{4}\) 

(iii) 7\(\frac{1}{3}\)

(iv) \(\frac{1}{3}\)

(v) 4\(\frac{1}{4}\)

(vi) \(\frac{5}{6}\)

(vii) 7\(\frac{4}{7}\)

(viii) 3\(\frac{9}{10}\)

(ix) \(\frac{1}{2}\)

(x) \(\frac{1}{10}\)

 Related Concepts




4th Grade Math Activities

From Subtraction of Unlike Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 03:45 PM

    Thousandths Place in Decimals
    When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…

    Read More

  2. Hundredths Place in Decimals | Decimal Place Value | Decimal Number

    Jul 20, 24 02:30 PM

    Hundredths Place in Decimals
    When we write a decimal number with two places, we are representing the hundredths place. Let us take plane sheet which represents one whole. Now, we divide the sheet into 100 equal parts. Each part r…

    Read More

  3. Tenths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 12:03 PM

    Tenth Place in Decimals
    The first place after the decimal point is tenths place which represents how many tenths are there in a number. Let us take a plane sheet which represents one whole. Now, divide the sheet into ten equ…

    Read More

  4. Representing Decimals on Number Line | Concept on Formation of Decimal

    Jul 20, 24 10:38 AM

    Representing decimals on number line shows the intervals between two integers which will help us to increase the basic concept on formation of decimal numbers.

    Read More

  5. Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

    Jul 20, 24 01:11 AM

    Decimal place value chart
    Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

    Read More